# Notations C

$\mathbb{C}$
complex plane; Common Notations and Definitions
$\subset$
is contained in; Common Notations and Definitions
$\subseteq$
is, or is contained in; Common Notations and Definitions
$C(\NVar{I})$ or $C(\NVar{a,b})$
continuous on an interval $I$ or $(a,b)$; §1.4(ii)
$C\left(\NVar{n}\right)$
Catalan number; (26.5.1)
$c\left(\NVar{n}\right)$
number of compositions of $n$; §26.11
$C\left(\NVar{z}\right)$
Fresnel integral; (7.2.7)
$C_{1}(\NVar{z})=C\left(\sqrt{2/\pi}z\right)$
alternative notation for the Fresnel integral; §7.1
$C_{2}(\NVar{z})=C\left(\sqrt{2z/\pi}\right)$
alternative notation for the Fresnel integral; §7.1
$c_{\NVar{k}}\left(\NVar{n}\right)$
Ramanujan’s sum; (27.10.4)
$C_{\NVar{\ell}}\left(\NVar{\eta}\right)$
normalizing constant for Coulomb radial functions; (33.2.5)
$c_{\NVar{m}}\left(\NVar{n}\right)$
number of compositions of $n$ into exactly $m$ parts; §26.11
$C_{\NVar{n}}\left(\NVar{x}\right)$
dilated Chebyshev polynomial; (18.1.3)
$\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)$
cylinder function; §10.2(ii)
$C^{\NVar{n}}(\NVar{I})$ or $C^{\NVar{n}}(\NVar{a,b})$
continuously differentiable $n$ times on an interval $I$ or $(a,b)$; §1.4(iii)
$C^{\infty}(\NVar{I})$ or $C^{\infty}(\NVar{a,b})$
infinitely differentiable on an interval $I$ or $(a,b)$; §1.4(iii)
$C^{(\NVar{\lambda})}_{\NVar{\alpha}}\left(\NVar{z}\right)$
Gegenbauer function; (15.9.15)
$C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}\right)$
ultraspherical (or Gegenbauer) polynomial; Table 18.3.1
$c\left(\NVar{\mathrm{condition}},\NVar{n}\right)$
restricted number of compositions of $n$; §26.11
$C_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)$
Charlier polynomial; Table 18.19.1
$C_{\NVar{n}}^{\NVar{m}}(\NVar{z},\NVar{\xi})$
Ince polynomials; §28.31(ii)
$c\left(\NVar{\epsilon},\NVar{\ell};\NVar{r}\right)$
irregular Coulomb function; (33.14.9)
$C(\NVar{f},\NVar{h})(\NVar{x})$
cardinal function; (3.3.43)
$C_{\NVar{n}}\left(\NVar{x};\NVar{\beta}\,|\,\NVar{q}\right)$
continuous $q$-ultraspherical polynomial; (18.28.13)
$\operatorname{cd}\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; (22.2.8)
$\mathit{cdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z},\NVar{k^{2}}\right)$
Lamé polynomial; (29.12.7)
$\operatorname{ce}_{\NVar{n}}\left(\NVar{z},\NVar{q}\right)$
Mathieu function; §28.2(vi)
$\operatorname{Ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$
modified Mathieu function; (28.20.3)
$\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z},\NVar{k^{2}}\right)$
Lamé polynomial; (29.12.3)
$\operatorname{ce}_{\NVar{\nu}}\left(\NVar{z},\NVar{q}\right)$
Mathieu function of noninteger order; (28.12.12)
$\mathrm{ceh}_{\NVar{n}}(\NVar{z},\NVar{q})=\operatorname{Ce}_{n}\left(z,q\right)$
notation used by Campbell (1955); §28.1
$\operatorname{cel}\left(\NVar{k_{c}},\NVar{p},\NVar{a},\NVar{b}\right)$
Bulirsch’s complete elliptic integral; (19.2.11)
$\chi\left(\NVar{n}\right)$
Dirichlet character; §27.8
$\chi(\NVar{x})$
ratio of gamma functions; §9.7(i)
$\operatorname{Chi}\left(\NVar{z}\right)$
hyperbolic cosine integral; (6.2.16)
$\operatorname{Ci}\left(\NVar{z}\right)$
cosine integral; (6.2.11)
$\operatorname{Ci}\left(\NVar{a},\NVar{z}\right)$
generalized cosine integral; (8.21.2)
$\operatorname{ci}\left(\NVar{a},\NVar{z}\right)$
generalized cosine integral; (8.21.1)
$\operatorname{Cin}\left(\NVar{z}\right)$
cosine integral; (6.2.12)
$\operatorname{cn}\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; (22.2.5)
$\mathrm{cn}(\NVar{z}\mathpunct{|}\NVar{m})=\operatorname{cn}\left(z,\sqrt{m}\right)$
alternative notation; §22.1
$\cos\NVar{z}$
cosine function; (4.14.2)
$\operatorname{Cos}_{\NVar{q}}\left(\NVar{x}\right)$
$q$-cosine function; (17.3.6)
$\operatorname{cos}_{\NVar{q}}\left(\NVar{x}\right)$
$q$-cosine function; (17.3.5)
$\cosh\NVar{z}$
hyperbolic cosine function; (4.28.2)
$\cot\NVar{z}$
cotangent function; (4.14.7)
$\coth\NVar{z}$
hyperbolic cotangent function; (4.28.7)
$\operatorname{cs}\left(\NVar{z},\NVar{k}\right)$
Jacobian elliptic function; (22.2.9)
$\csc\NVar{z}$
cosecant function; (4.14.5)
$\operatorname{csch}\NVar{z}$
hyperbolic cosecant function; (4.28.5)
$\operatorname{curl}$
of vector-valued function; (1.6.22)